Revision History for A225431
(Underlined text is an addition;
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Showing entries 1-10
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#36 by T. D. Noe at Tue May 14 12:59:01 EDT 2013
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#35 by T. D. Noe at Tue May 14 12:58:54 EDT 2013
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| MATHEMATICA
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nn = 1000; ta = LinearRecurrence[{4, -1}, {1, 3}, 1000nn]; tb = LinearRecurrence[{4, -1}, {1, 5}, 1000nn]; sol = Select[Range[1000nn], PrimeQ[ta[[#]]] && PrimeQ[tb[[#]]] &]; tta[[sol]] (* T. D. Noe, May 14 2013 *)
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#34 by T. D. Noe at Tue May 14 12:56:20 EDT 2013
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This is a form of Pell's equation with the requirement that solutions be prime. - T. D. Noe, May 14 2013
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Eric W. Weisstein, <a href="http://mathworld.wolfram.com/PellEquation.html">MathWorld: Pell Equation</a>
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ta = LinearRecurrence[{4, -1}, {1, 3}, 1000]; tb = LinearRecurrence[{4, -1}, {1, 5}, 1000]; sol = Select[Range[1000], PrimeQ[ta[[#]]] && PrimeQ[tb[[#]]] &]; t[[sol]] (* T. D. Noe, May 14 2013 *)
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| STATUS
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approved
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#33 by Bruno Berselli at Tue May 14 05:04:25 EDT 2013
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#32 by Michael B. Porter at Mon May 13 21:29:31 EDT 2013
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#31 by Michael B. Porter at Mon May 13 21:28:43 EDT 2013
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#30 by Michael B. Porter at Mon May 13 21:26:47 EDT 2013
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(PFGW)
(PFGW) ABC2 Linear(3, 11, 41, 153, $a) & Linear(5, 19, 71, 265, $a)
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#29 by Michael B. Porter at Mon May 13 21:24:40 EDT 2013
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| EXAMPLE
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311 is prime and sqrt(3*311^2 - 2) = sqrt(25361) = 519 is prime, so 11 is in the a(1) = 3;sequence.
11 prime and sqrt(3*11^2 - 2) = sqrt(361) = 19 prime, so a(2) = 11;
41 prime and sqrt(3*41^2 - 2) = sqrt(1681) = 71 prime, so a(3) = 41.
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| PROG
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(PFGW) ABC2 Linear(3, 11, 41, 153, $a) & Linear(5, 19, 71, 265, $a) // _Charles R Greathouse IV_, May 13 2013)
a: from 3 to 20000 // _Charles R Greathouse IV_, May 13 2013
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proposed
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#28 by Charles R Greathouse IV at Mon May 13 14:12:21 EDT 2013
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#27 by Charles R Greathouse IV at Mon May 13 14:11:59 EDT 2013
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| COMMENTS
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Probably finite.
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| PROG
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(PARI) v=[1, 1]; for(i=1, 1e4, v=[v[2], 4*v[2]-v[1]]; if(ispseudoprime(v[2]) && ispseudoprime(sqrtint(3*v[2]^2-2)), print1(v[2]", "))) \\ Charles R Greathouse IV, May 13 2013
(PFGW) ABC2 Linear(3, 11, 41, 153, $a) & Linear(5, 19, 71, 265, $a) // Charles R Greathouse IV, May 13 2013
a: from 3 to 20000
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proposed
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